Updated July 29, 2023

##### Exponential Growth Formula (Table of Contents)

- Exponential Growth Formula
- Examples of Exponential Growth Formula (With Excel Template)
- Exponential Growth Calculator

## Exponential Growth Formula

Exponential growth and decay are the two functions to determine the growth and decay in a stated pattern. Exponential growth and decay formula can be used in a particular situation if a quantity grows at regular intervals, the pattern of the function can be depicted and summarised in an algebraic equation.

The exponential growth formula can be mentioned as:-

**Exponential Growth (y) = a * (1 + r) ^x**

Whereas on the other hand exponential decay formula can be mentioned as

**Exponential Decay (y) = a * (1 – r) ^x**

Where the following integers can be stated as:-

**a**= Initial growth (the amount before measuring growth or decay)**r**= Growth or Decay rate (most often represented as a percentage and expressed as a decimal)**x**= Number of time intervals that have passed

### Examples of Exponential Growth Formula (With Excel Template)

Let’s take an example to understand the calculation of Exponential Growth in a better manner.

#### Exponential Growth – Example #1

**The population of a hometown in Scotland in 2019 was estimated to be 35,000 in that year. The population is expected to grow with an annual increase of 2.4% every year. What is the growth factor of home town in Scotland and use the estimate to calculate the population of the hometown for the next 4 years?**

**Solution:**

Exponential Growth is calculated using the formula given below

**Exponential Growth (y) = a * (1 + r) ^x**

- Exponential Growth = 35,000 * (1+ 2.4%)^4
- Exponential Growth =
**38,482.91**

Exponential Growth is **38,482.91**

#### Exponential Growth – Example #2

**In 2021 there are around 3000 inhabitants in a small remote village near the Himachal area. The average annual growth rate of population in the past 3 years is 12% every year. How many residents will be there in the village after 10 years? Need to calculate the value through the exponential growth.**

**Solution:**

Exponential Growth is calculated using the formula given below

**Exponential Growth (y) = a * (1 + r) ^x**

- Exponential Growth = 3,000 * (1 + 12%) ^3
- Exponential Growth =
**4,214.78**

Exponential Growth is **4,214.78.**

#### Exponential Growth – Example #3

**A certain type of bacteria, given a favorable grows at a rate of 10%. Given that there were approximately 100 bacteria to start with, how many bacteria will there be in a day and a half?**

**Solution:**

Exponential Growth is calculated using the formula given below

**Exponential Growth (y) = a * (1 + r) ^x**

- Exponential Growth = 100 * (1 + 10%) ^36
- Exponential Growth =
**3,091.27**

Exponential Growth is **3,091.27.**

### Explanation

The formula is used where there is continuous growth in a particular variable such population growth, bacteria growth, if the quantity or can variable grows by a fixed percentage then the exponential formula can come in handy to be used in statistics

### Relevance and Uses of Exponential Growth Formula

- The concept of exponential growth is mostly used in the concept of modeling and the growth of economics. If we want to find what will be the revenue of the company if it is a growing at a constant rate of x% then we often use the exponential growth and its concept to determine the revenue of the company which is growing at a certain percentage of growth rate
- The exponential function also appears in a variety of contexts within physics, chemistry, engineering, mathematical biology, and economics also it is prevalent in natural and social science concepts
- The exponential formula is an important function in mathematics also and it has been derived from the help of mathematics and economics only. The exponential decay formula is useful in a variety of real-world applications, most notably for tracking inventory that’s used regularly in the same quantity (like food for a school cafeteria) and it is especially useful in its ability to quickly assess the long-term cost of use of a product over time

### Exponential Growth Calculator

You can use the following Exponential Growth Calculator

a | |

r | |

x | |

Exponential Growth(y) Formula | |

Exponential Growth(y) Formula = | a * (1 + r)^{x} |

= |
0 * (1 + 0)^{0} =
0 |

### Recommended Articles

This has been a guide to Exponential Growth formula. Here we discuss how to calculate Exponential Growth along with practical examples. We also provide an Exponential Growth calculator with downloadable excel template. You may also look at the following articles to learn more –